AI 中文总结
该研究通过熵方法分析锥上的加权Carlson-Levin不等式，获其最优常数与最优解分类，推导出加权Gagliardo-Nirenberg不等式的刚性结果，给出单项式权相关示例。
AI 中文摘要
我们研究锥上的加权Carlson-Levin不等式，通过熵方法计算最优常数并分类最优解，还处理了对数Carlson-Levin不等式的极限情形。作为推论，我们得到加权Gagliardo-Nirenberg不等式的刚性结果，最后给出含单项式权的若干例子。
英文摘要
We study weighted Carlson-Levin inequalities on cones, computing the optimal constant and classifying optimizers via an Entropy method. The limiting case of a logarithmic Carlson-Levin inequality is also treated. As a Corollary, we obtain a rigidity result for a weighted Gagliardo-Nirenberg inequality. We conclude with some examples involving monomial weights.
Comments20 pages
